Application and convergence analysis of mixed quadrature rule for approximate solution of product integral

Saumya Ranjan Jena; Madhusmita sahoo; Prasanta Kumar Mohanty; Satya Kumar Misra; Bhupati Bhusan Mishra

Saumya Ranjan Jena KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India
Madhusmita sahoo KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India
Prasanta Kumar Mohanty KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India
Satya Kumar Misra KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India
Bhupati Bhusan Mishra KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India

Abstract

This investigation presents a mixed quadrature rule of precision level eleven by consolidating different kinds of Newton's and Gaussian rule of lower accuracy by eliminating end point singularity on the product intgration of the improper integral.The mixture format of cubic Newton's divided difference and the Romberg technique are employed on different classes of functions for product integration.An error bound is obtained utilizing mixed quadrature.Two mathematical models and convergence analysis are explored to legitimize the efficiency and accuracy of the current scheme in contrast with existing methods.